J-‘s now on her summer break. We’ve been thinking of ways to help her use her summer well. There’ll be time for unstructured play and for hanging out with friends, of course, but it’s also good to help her develop initiative and life skills, fighting the temptations of video games along the way.

Both W- and I are working through summer because we’re saving our vacation days for Kathy’s upcoming wedding, so J- will need to be self-driven. She’s pretty good at dealing with the inevitable what-do-I-do-now moments (and we all get those, if we’re lucky). She often practises piano or ukulele, reads a book, or hangs out with friends. We can help by setting some challenges, nudging her to work on mastery or life skills, and giving her feedback on how she’s doing (such as for writing or math exercises).

Overall plans for the summer:

Read

Practise music

Hang out with friends

Prepare for next school year

Work on life skills

It’s often easier to pick from a list than to think of something to do in the moment, so here are some ideas for things to do:

Physical

Swimming

Biking

Exercising

Running, playing in the park

Mental

Reading a book (critical reading – maybe discussion at dinner?)

Working on reading exercises

Working on math exercises

Going to the library

Creative

Drawing (comics, sketches, etc.) – maybe put together a sketchbook or comic book

Writing notes, stories, and so on

Playing the piano or the ukulele

Visiting the AGO, the ROM, the science centre, etc.

Taking pictures

Exploring arts and crafts (ex: collage, sculpting)

Life skills

Learning how to cook

Making life better: cleaning, tidying, looking for ways to improve, etc.

Volunteering (Free Geek?)

Learning life skills: taking public transit, biking, etc.

Negotiating/persuading

Play

Hang out with friends

Play video games (time-limited?)

Play board games

We’ll encourage her to add to this list, too.

We like the way her school uses rubrics to make it clear what excellence looks like. We’re not planning to use one to grade J- for her summer work – grading summer! what a thought – but it might be useful to work out one with her so that she can self-evaluate how she’s spending her time and so that she can motivate herself to push her limits. W- and I thought about the process first so that we can guide her through planning her own. Here’s the draft W- and I came up with:

Category

1

2

3

4

Physical

Sat on couch all day / stayed indoors

Basic calisthenics

Extended physical activity

Stretching your limits

Mental

Played video games all day / watched TV all day

1 unit of work

2 units of work

3 units of work

Creative

No creative output

Drew / wrote / practised piano/ukulele / etc.

Memorized part of a song / New story/comic/drawing to share

Discussion of work

Life skills

Mess

Cleaned up after self

Cleaned up after cats

Made life better / cleaned up after others

Technology

Played video games or surfed the Internet all day

Practised IT skills (typing, presentations, etc.)

Created something using technology and shared it with us or others

Learned something on your own / experimented with tools

Thinking of ways to build scaffolds for J-‘s learning through these lists of ideas and rubrics for self-evaluation inspires me to make some of these for myself, too.

What would my discretionary-time activities look like?

Physical

Biking

Exercising

Gardening

Mental

Reading a book, maybe blogging notse

Improving development skills

Creative

Drawing – sketches, presentations, etc.

Writing notes, stories, blog posts

Playing the piano

Visiting the AGO, the ROM, the science centre, etc.

Taking pictures

Life skills

Preparing a new recipe or experimenting with a familiar one

Making life better: cleaning, tidying, looking for ways to improve, etc.

J- brought home her report card this week. She did well in so many subjects that it’s hard to pick which strength to build on first. Her mathematics study group sessions and science projects paid off, as did her personal interest in music.

To celebrate her work, W- and I made a colourful card. She likes making greeting cards for us, and it was fun making one for her.

It’s important to acknowledge good work. One time, W- was reviewing J-‘s answers to the math exercises he gave her. “Very good,” he said. He crumpled the finished piece of paper.

I plucked it from his hands and smoothened it out. “Ahem,” I said meaningfully.

“Oops. I tossed the other one already,” confessed W-. I retrieved the previous paper from the recycling bin and uncrumpled it. W- made a point of scoring both papers and adding smileys. J- beamed.

Ah, behavioural psychology at home. You can influence people’s motivation by acknowledging or devaluing their work. In The Upside of Irrationality: The Unexpected Benefits of Defying Logic at Work and at Home (Dan Areily, 2010), I read about experiments that explored how motivated people were if they thought their results were meaningless. As it turns out, people are strongly affected by the immediate perception of the usefulness of their work.

In a task involving assembling Lego figures, participants who completed figures and put them into a box did more and enjoyed the task more than participants whose figures were disassembled right after they finished completing them. Another experiment described in the book involved finding pairs of letters on pages, a small payment scheme that stopped at the 10th sheet, and three scenarios where:

people wrote their names on the papers they completed, and they were positively acknowledged by the experimentr

people completed and submitted papers with no names and without acknowledgement

people submitted papers that were then shredded, unread, right in front of them

49% of the people who were acknowledged went on to complete ten sheets or more, while only 17% of the people whose work was immediately shredded completed 10 or more. Only 18% of the people whose work was ignored completed ten sheets or more.

Verbal acknowledgment of good work is good, but could it be at odds with the physical message of tossing the paper into the recycling bin? Best to be coherent. So the paper is celebrated, labeled, and put into a folder.

W- reminds me of this principle too, when I forget. On the way home from work one day, I brought up how he spent some time selecting and copying items from the workbook onto a piece of paper for J-‘s exercises. “Should we get a workbook without explanations, so J- can test herself?” I asked W-.

“No, it’s okay. Besides, it shows her that I value this,” W- said. “If I give her a workbook so that I can do something else, it’s not the same.”

Flashcards are great for memorizing. They break topics down into learnable chunks, develop random-access knowledge, and turn learning into a game with visual progress. Flashcards also make it easier for people to learn together, testing each other on concepts.

We’ve been teaching the kids in the study group using flashcards for multiplication facts, fractions, and the Greek alphabet. We also teach them how to use cognitive theory to improve learning–well, perhaps not in those words. For example, when J- wants to help her friends learn the Greek alphabet (having handily mastered recognition herself), we encouraged her to cycle through letters in small sets (5 to 7 characters at a time) instead of running through all the letters in one go. It’s the same technique we used when they were learning the multiplication table.

J- also shared the mnemonics she used to remember many of the Greek letters. For example, she described λ as “Lambda, like Mary had a little lamb, going down a hill.” They’re quickly developing in-jokes, too, like the way V- calls α Pisces, they call Μ big mu, and ω makes the kids laugh.

W- and I have our own flashcards: Dutch, in preparation for our upcoming trip, and Latin, because we’re learning that too. Electronic flashcards offer convenience, of course, but paper flashcards are so much more fun.

In this week’s study group, we plan to teach the kids about the Leitner system for flashcard efficiency. I found out about the Leitner system by reading the comments in the Emacs flashcard.el mode years ago, when I was learning Japanese. The Leitner system optimizes learning by reducing the repetitions for cards you know well and increasing the repetitions for cards you answer incorrectly. It works like this:

Start with your flashcards in one group (group 1). Review the cards in a group. If you answer a card correctly, move it to one group higher. If you answer a card incorrectly, move it back to group 1. Repeat with each group of cards. When you answer a card in group 5 correctly, you can archive the card until you want to do a general review again. This weeds out the cards that you can correctly answer five times in a row and lets you focus on the cards that you can’t consistently answer.

I think the Leitner system is really cool. It’s an elegant algorithm with a physical implementation. Neat!

From April 26, Tuesday: J-‘s studying for Thursday’s “in-class performance assessment” on integers. (In-class performance assessment? What happened to the good old word “quiz?” Too much anxiety?) We’re spreading the review out over the next two evenings.

The test will cover adding and subtracting positive and negative numbers. J- and her study group are already off multiplying and dividing (which apparently don’t turn up until grade 8 – really?). W- made up a quick worksheet for J- to practise adding, subtracting, multiplying, and dividing integers.

“The enemy of your enemy is your friend,” I heard her say as she solved the exercises, writing down the correct signs for all the products and quotients. I grinned. I’d taught them that mnemonic two weeks ago. It’s a way to remember the results of multiplying or dividing numbers.

As I explained to the kids: you don’t have to stick to this in real life. Pou can certainly be friends with the friends of your enemy. But this might help you remember the signs for multiplication and division:

The friend of your friend is your friend. Positive times positive is positive.

The friend of your enemy is your enemy. Positive times negative is negative.

The enemy of your friend is your enemy. Negative times positive is negative.

The enemy of your enemy is your friend. Negative times negative is positive.

A

B

Result

Friend +

Friend +

Friend +

Friend +

Enemy –

Enemy –

Enemy –

Friend +

Enemy –

Enemy –

Enemy –

Friend +

2011-04-26 Tue 20:05

Glad to see it stuck in her head! She answered all the exercises correctly (and quickly, too).

It was Friday, so J- and her friends were singing the Friday song as they hung up their coats and got ready for our math study group. It turned out that they had been so excited about coming home (to a math study group!) that they’d forgotten to arrange things with their parents, and V-‘s dad had been waiting for her at school. Once everyone had called around and sorted things out with their parents, and everyone was well-fed, we got back to math.

One of the benefits of hosting multiple kids in a study group is that you get more information about what people are learning in school. V- said she needed help with positive and negative numbers, so that’s what we started off reviewing.

A quick review: 2 – (-3) = ? . Boggles all around.

Okay. A step down: -2 – 4 = ?. Still boggles and some guesses.

I drew a number line and labelled it with the numbers. “Imagine a cat standing on -2. Which direction does the cat go if you’re subtracting 4?”

“Left!” chorused the kids. “-6!”

I drew the cat ending up on -6. We did a couple of other exercises along those lines. Nods all around. Okay.

“What about -2 + 3?” I drew another numberline. “Right! +1.”

“What about 2 – (-3)?” I drew the cat on the numberline. “Okay, we’re starting on 2. And we’re subtracting, so we would normally move to the left, but we’re moving -3 steps… so the cat walks backward three steps.”

“5!” said the kids. One of them asked, “Do your cats really walk backwards?”

“They do more of this hopping backward thing, yes, but cats can walk backwards if they want to.”

So we did a few more of those exercises, including things like -4 – (-5) and -(-(-2)). We also reviewed multiplying and dividing positive and negative numbers. The kids seemed comfortable with that, and answered our exercises with little prompting.

As we wrapped up our review of positive and negative numbers, A- arrived. She’s in grade 6, a grade behind the other kids, so we modified our exercises. She said she was taking up decimals in class. I asked her how she felt about the multiplication table. “Bad,” she confessed, at which the other kids begged (begged!) to do multiplication practice.

“But first, we’re going to talk about algebra very quickly,” W- said. He briefly reviewed what an algebraic equation really means, and the different parts of the equation: the constants, the variables, the operators, the assertion, and so on. We hope this will help them remember to keep their equations balanced, always doing operations on both sides of the equals sign.

“All right, multiplication,” I said, and we headed outside to practise multiplication. The way we do it is good for building confidence and a sense of numbers: we go through sets of five multiples until the kids can rattle them off smoothly. For example: 6, 12, 18, 24, 30. 6, 12, 18, 24, 30. And so on, around the circle. It’s really more of an audio recall task than a calculation task, and it gets them used to what the numbers feel like. They catch themselves now, when they make a mistake. And they’re enthusiastic and run ahead of themselves, doing sets of ten instead of sets of five, or challenging themselves further by doing jumping jacks while saying the numbers.

After multiplication practice, one of the kids piped up and asked, “Can we solve the equation in the breadbox?” Ah. Yes. Those. I’d spent some time the night before writing up simple equations and hiding them around the first floor of the house – possible exercises for J- or the study group, depending on how things went. So we agreed that they could look for the five Post-It notes I’d hidden IF they solved the equations as well. I settled in to review decimal multiplication and division with A- to help her catch up, and W- reviewed the other kids’ work on the algebraic equations.

Our Friday afternoon math study groups are a great ritual. Glad we stumbled into organizing them! I hope other parents can host study groups as well – it would be good for all the kids to see active involvement – but it’s probably easiest for us, logistically speaking, because we can often work from home and we both enjoy teaching. If you can, try it!

Stian Håklev is passionate about education – and in particular, the richness of different cultures and perspectives. Here are some notes from a fascinating conversation I had with him at the Ontario Institute for Studies in Education, where he’s doing his PhD.

Stian’s passionate about open access, open research, multiculturalism, peer-to-peer education, and other interesting things. He’s hooked into Mozilla Foundation and the Center for Social Innovation. What else can he look at and who can he talk to? Possibly related: Open Notebook Science, LearnHub, Third Culture Kids, DemoCampToronto (to show his peer-to-peer education site and ask for tips?)

Do these questions strike a chord with you? Get in touch with Stian and make cool stuff happen! reganmian.net